Micro channels are used in heat exchangers and applications in medicine, consumer electronics, avionics, metrology, robotics, industry processes, telecommunications, automotive and other areas. The thermal performance of a micro channel depends on the geometric parameters and flow conditions defining the micro channel environment. Prior art attempts using analytical or numerical techniques to determine the optimal dimensions of micro channels assume that the aspect ratio of the micro channels is known a priori. The present invention determines the optimum geometric parameters of micro channels in micro heat exchangers by combining computational fluid dynamics (CFD) analyses and an analytical method of calculating the optimum geometric parameters of micro heat exchangers. CFD is used in determining the optimal aspect ratio and an analytical approximation is employed to calculate optimal micro heat exchanger dimensions based on the determined optimal aspect ratio.
A heat exchanger is referred to as a micro heat exchanger when the surface area density is greater than 10000 m2/m3 on at least one of the fluid sides. [Shah, R. K., Compact heat exchanger technology and applications, in E. A. Foumeny, P. J. Heggs (Ed.), Heat Exchange Engineering, E. Horwood, New York, 1991, chap. 1.] Micro channel heat exchangers combine the attributes of a high surface area to volume ratio, a large convective heat transfer coefficient, and small mass and volume. Early work proposed micro channel heat sinks based on the idea that the heat transfer coefficient is inversely proportional to the hydraulic diameter of the channel. [D. B. Tuckerman, R. F. W. Pease, High-performance heat sinking for VSLI, IEEE Electron Dev. 2 (1981) 126–129]. High heat transfer coefficients are achievable with small hydraulic diameters since the heat transfer coefficient is inversely proportional to the hydraulic diameter; thus, micro channels have high heat flux capacity.
In micro channels: 1) a small cross-sectional area of a micro channel reduces the thickness of a thermal and hydraulic boundary layers; the resultant effect is that the heat transfer coefficient, h, is several times higher than the thermal conductance of a stationary layer; 2) the heat transfer coefficient is higher in the thermally developing region where the thermal boundary layer is thin; in micro channels most, if not all, of the micro channel is in the thermally developing region where h is high; 3) micro channel passages have sharp-edge entrances; pre-turbulence at the sharp-edged inlets delays development of the thermal boundary resulting in thinner thermal boundary layer, and hence, a higher heat transfer coefficient; and 4) as a result of the small scale of micro channel passages, wall roughness plays an important role in increasing the heat transfer coefficient.
A disadvantage of the micro channel as a fluid flow device is the high pressure loss associated with a small hydraulic diameter. In order to take maximum advantage of the micro channel, there must be a balance between the desirable high heat transfer coefficient and the undesirable pressure loss.
Experimental, analytical and numerical studies have referred to deviations in the heat transfer and fluid flow characteristics of micro-scale devices from those of conventionally-sized (or macro-scale) devices. Flow and heat transfer characteristics of fluids flowing in micro channels could not be adequately predicted by theories and correlations developed for conventionally-sized channels. For example, studies showed that the performance of a micro channel heat exchanger depends very much on the aspect ratio (AR) of the channels. [J. B. Aparecido, R. M. Cotta, Thermally developing laminar flow inside rectangular ducts, Int. J. Heat Mass Transfer 33 (2) (1990) 341–347, and X. Wei, Y. Joshi, Optimization of stacked micro-channel heat sinks for micro-electronic cooling, Inter Society Conf. On Thermal Phenomena (2002) 441–448.]
Optimization studies to minimize temperature gradient and overall thermal resistance in micro channels suggested that reduction in overall thermal resistance could be achieved by varying the cross-sectional dimensions of a channel. [H. H. Bau, Optimization of conduits' shape in micro heat exchangers, Int. J. Heat Mass Transfer 41 (1998) 2117–2723].
Prior attempts to design micro heat exchangers and reactors, for example, in the process and automotive industries, may be classified as analytical and numerical methodologies. In analytical studies, the primary objective is to design schemes to optimize the channel dimensions in micro heat exchangers by maximizing heat transfer for a given pressure drop. In such an optimization scheme, a mathematical description of the transport processes in the micro channel is required; however, the complex heat transfer process in micro channels coupled with the flow makes it practically impossible to solve analytically the conservation equations that describe the fluid flow and heat transfer phenomenon. In most analytical studies, equations are reduced to tractable forms by simplifying assumptions that compromise the accuracy of predictions. To accurately predict fluid flow and heat transfer phenomena in micro channels, a numerical solution of the complete form of the conservation equations must be solved numerically.
Another approach combines computational fluid dynamics numerical simulation (CFD) with an optimization strategy to determine the optimal shape of a micro channel heat sink that minimizes the thermal resistance. [J. H. Ryu, D. H. Choi, S. J. Kim, Numerical optimization of the thermal performance of a micro channel heat sink, Int. J. Heat Mass Transfer 45 (2002) 2823–2827]. In this approach, however, the optimal geometric parameters were determined based on an assumed aspect ratio of the micro channels.
It is an object of this invention to provide optimal micro channels in micro heat exchangers that maximize the heat transfer rate (or heat flux) subject to specified design constraints. The invention optimizes the geometric parameters based on an optimal aspect ratio of the micro channels of the micro heat exchanger. Although the examples herein relate to gas flow (nitrogen and carbon dioxide) and an Inconel® micro channel heat exchanger, the methods, systems, and configurations herein similarly apply to other fluids and high-conductivity solids.
The invention is described more fully in the following description of the preferred embodiment considered in view of the drawings in which: